Monday, November 26, 2007

There's been quite a lot of reaction to a New York Times op-ed by Paul Davies titled Taking Science on Faith. (I read about it first on Adventures in Ethics and Science.) Davies argues that, like religion, science is ultimately based on faith. My main interest is not in his argument per se (but see here for some scathing critiques).

What struck me about Davies' essay was his use of the term scientific law. He uses it again and again, whereas he refers to a theory only twice, and not once does he refer to a model.

If there are laws, then presumably there's a lawmaker, and the obvious candidate would be God. If we are able to discover these laws, then we have identified Truth. Who can then disagree? Who can go against the law?

This seems to me a very arrogant notion. In fact the history of science is littered with "laws" that have subsequently been overturned or shown to be special cases or approximations. For instance, Newton's laws of motion (one of which, incidentally—his 2nd law, F=ma—is actually a definition) were superceded by special relativity and quantum mechanics.

I would concede that in principle, it may be possible to get a model exactly right, but except in the case of a computer simulation, it isn't possible to be certain that it's right! To me, Box's aphorism is humble, epistemologically wise, and profoundly scientific.

It is my impression that for many years now there has been a movement in science away from the word law, with its implicit suggestion that the Truth has been definitively uncovered, and that somehow any deviation from the law is improper or even unimaginable. Nevertheless, use of the term continues (see the Wikipedia entries for scientific law, physical law, and laws of science). It might be argued that I'm reading too much into the word law. But consider how it affects schoolchildren who are learning about science. Rather that encouraging the idea that science is about curiousity, observing, investigating, and testing, I think it suggests that science is about memorizing rules.

Laws of chance

There is another class of "laws" that aren't exactly scientific, but still have an empirical aspect. In probability and statistics, it was at one time common to refer to probability "laws", the most famous being the curiously-named normal law. Today we refer to it as the normal distribution, or better yet the Gaussian distribution. The term "normal law" is a bit of a double-whammy: to go against it you would have to be abnormal and lawless!

Two fascinating "laws" relating to probability distributions are Zipf's law and Benford's law. I think that what makes probability distributions seem like "laws" is that they often hold—at least approximately—under quite general real-world conditions.

Law-abiding citizens

Why are we so prone to label models (among other things) as laws? I think it might be related to our abhorrence of uncertainty. For a law-abiding citizen, laws are a source of security. Everything seems neat and tidy and safe and predictable. But every so often, the world is revealed to be a bit different from what we expected. Maybe the laws don't work so well after all ...